Characterization of the interior regularity for parabolic systems with discontinuous coefficients

Dian K. Palagachev; Lubomira G. Softova

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2005)

  • Volume: 16, Issue: 2, page 125-132
  • ISSN: 1120-6330

Abstract

top
We deal in this Note with linear parabolic (in sense of Petrovskij) systems of order 2 ⁢ b with discontinuous principal coefficients belonging to V ⁢ M ⁢ O ⁢ ⋂ L ∞ . By means of a priori estimates in Sobolev-Morrey spaces we give a precise characterization of the Morrey, BMO and Hölder regularity of the solutions and their derivatives up to order 2 ⁢ b - 1 .

How to cite

top

Palagachev, Dian K., and Softova, Lubomira G.. "Characterization of the interior regularity for parabolic systems with discontinuous coefficients." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 16.2 (2005): 125-132. <http://eudml.org/doc/252397>.

@article{Palagachev2005,
abstract = {We deal in this Note with linear parabolic (in sense of Petrovskij) systems of order $2b$ with discontinuous principal coefficients belonging to $VMO \bigcap L^\{\infty\}$. By means of a priori estimates in Sobolev-Morrey spaces we give a precise characterization of the Morrey, BMO and Hölder regularity of the solutions and their derivatives up to order $2b-1$.},
author = {Palagachev, Dian K., Softova, Lubomira G.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Parabolic systems; A priori estimates; Morrey spaces; Hölder regularity; VMO; parabolic systems; a priori estimates},
language = {eng},
month = {6},
number = {2},
pages = {125-132},
publisher = {Accademia Nazionale dei Lincei},
title = {Characterization of the interior regularity for parabolic systems with discontinuous coefficients},
url = {http://eudml.org/doc/252397},
volume = {16},
year = {2005},
}

TY - JOUR
AU - Palagachev, Dian K.
AU - Softova, Lubomira G.
TI - Characterization of the interior regularity for parabolic systems with discontinuous coefficients
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/6//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 2
SP - 125
EP - 132
AB - We deal in this Note with linear parabolic (in sense of Petrovskij) systems of order $2b$ with discontinuous principal coefficients belonging to $VMO \bigcap L^{\infty}$. By means of a priori estimates in Sobolev-Morrey spaces we give a precise characterization of the Morrey, BMO and Hölder regularity of the solutions and their derivatives up to order $2b-1$.
LA - eng
KW - Parabolic systems; A priori estimates; Morrey spaces; Hölder regularity; VMO; parabolic systems; a priori estimates
UR - http://eudml.org/doc/252397
ER -

References

top
  1. AGMON, S. - DOUGLIS, A. - NIRENBERG, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math., vol. 12, 1959, 623-727. Zbl0093.10401MR125307
  2. AGMON, S. - DOUGLIS, A. - NIRENBERG, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Comm. Pure Appl. Math., vol. 17, 1964, 35-92. Zbl0123.28706MR162050
  3. CAMPANATO, S., Proprietà di Hölderianità di alcune classi di funzioni. Ann. Scuola Norm. Sup. Pisa, vol. 17, 1963, 175-188. Zbl0121.29201MR156188
  4. CHIARENZA, F. - FRANCIOSI, M. - FRASCA, M., L p -Estimates for linear elliptic systems with discontinuous coefficients. Rend. Mat. Acc. Lincei, s. 9, vol. 5, 1994, 27-32. Zbl0803.35016MR1273890
  5. DA PRATO, G., Spazi L p , θ ⁢ Ω , δ e loro proprietà. Ann. Mat. Pura Appl., vol. 69, 1965, 383-392. Zbl0145.16207MR192330
  6. DOUGLIS, A. - NIRENBERG, L., Interior estimates for elliptic systems of partial differential equations. Comm. Pure Appl. Math., vol. 8, 1955, 503-538. Zbl0066.08002MR75417
  7. EJDEL'MAN, S.D., Parabolic Equations. In: YU.V. EGOROV - M.A. SHUBIN (eds.), Partial Differential Equations VI: Elliptic and Parabolic Operators. Encycl. Math. Sci., vol. 63, Springer-Verlag, Berlin1994, 203-316. Zbl0802.35061MR1313734DOI10.1007/978-3-642-57876-2
  8. FABES, E.B. - RIVIÈRE, N., Singular integrals with mixed homogeneity. Studia Math., vol. 27, 1966, 19-38. Zbl0161.32403MR209787
  9. FRIEDMAN, A., Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, N.J., 1964. Zbl0144.34903MR181836
  10. JOHN, F. - NIRENBERG, L., On functions of bounded mean oscillation. Comm. Pure Appl. Math., vol. 14, 1961, 415-426. Zbl0102.04302MR131498
  11. KRONZ, M., Some function spaces on spaces of homogeneous type. Manuscr. Math., vol. 106, 2001, 219-248. Zbl0989.43004MR1865566DOI10.1007/s002290100205
  12. MAUGERI, A. - PALAGACHEV, D.K. - SOFTOVA, L.G., Elliptic and Parabolic Equations with Discontinuous Coefficients. Wiley-VCH, Berlin2000. Zbl0958.35002MR2260015DOI10.1002/3527600868
  13. PALAGACHEV, D.K. - SOFTOVA, L.G., Singular integral operators, Morrey spaces and fine regularity of solutions to PDE's. Potential Anal., vol. 20, 2004, 237-263. Zbl1036.35045MR2032497DOI10.1023/B:POTA.0000010664.71807.f6
  14. SARASON, D., Functions of vanishing mean oscillation. Trans. Amer. Math. Soc., vol. 207, 1975, 391-405. Zbl0319.42006MR377518
  15. SOLONNIKOV, V.A., On the boundary value problems for linear parabolic systems of differential equations of general form. Proc. Steklov Inst. Math., vol. 83, 1965 (in Russian); English translation: O.A. LADYZHENSKAYA (ed.), Boundary Value Problems of Mathematical Physics III. Amer. Math. Soc., Providence, R.I., 1967. Zbl0164.12502

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.